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Convolutional Analysis Operator Learning: Acceleration and Convergence.
- Source :
- IEEE Transactions on Image Processing; 2020, Vol. 29, p2108-2122, 15p
- Publication Year :
- 2020
-
Abstract
- Convolutional operator learning is gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called patch-domain approaches that extract and store many overlapping patches across training signals. Due to memory demands, patch-domain methods have limitations when learning kernels from large datasets – particularly with multi-layered structures, e.g., convolutional neural networks – or when applying the learned kernels to high-dimensional signal recovery problems. The so-called convolution approach does not store many overlapping patches, and thus overcomes the memory problems particularly with careful algorithmic designs; it has been studied within the “synthesis” signal model, e.g., convolutional dictionary learning. This paper proposes a new convolutional analysis operator learning (CAOL) framework that learns an analysis sparsifying regularizer with the convolution perspective, and develops a new convergent Block Proximal Extrapolated Gradient method using a Majorizer (BPEG-M) to solve the corresponding block multi-nonconvex problems. To learn diverse filters within the CAOL framework, this paper introduces an orthogonality constraint that enforces a tight-frame filter condition, and a regularizer that promotes diversity between filters. Numerical experiments show that, with sharp majorizers, BPEG-M significantly accelerates the CAOL convergence rate compared to the state-of-the-art block proximal gradient (BPG) method. Numerical experiments for sparse-view computational tomography show that a convolutional sparsifying regularizer learned via CAOL significantly improves reconstruction quality compared to a conventional edge-preserving regularizer. Using more and wider kernels in a learned regularizer better preserves edges in reconstructed images. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10577149
- Volume :
- 29
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Image Processing
- Publication Type :
- Academic Journal
- Accession number :
- 170078025
- Full Text :
- https://doi.org/10.1109/TIP.2019.2937734